Method for cancelling a narrow-band interference signal

ABSTRACT

A method of canceling a narrow-band interference signal in a receiver is provided. A reference signal (ref_in) is subtracted from a received input signal (in). the phase of a result of the subtraction is calculated on the basis of an arctangent function. An unwrap function on the output signal from the arctangent function is performed by removing the modulo 2Π limitation introduced with the arctangent function, in order to produce an absolute phase representation. A frequency offset is determined by comparing phase representation values which are shifted predetermined in time. The narrow-band interference signal is canceled based on the result of the determined frequency offset.

This invention relates in general to the field of radio communicationsand more specifically to interference cancellation/suppression of anarrow band interferer in a wide band communication device.

Wireless computing has experienced an enormous growth since it allowsusers to access network services without being bounded to a wiredinfrastructure. Due to the rapid growth of wireless networks in recentyears, problems with different networks interfering with each other haverisen. These problems become significant when networks occupy the samefrequency band, causing them to interfere with each other. The twowireless systems that have experienced the most rapid evolution and widepopularity are the standard developed by IEEE for wireless local areanetworks (WLANs), identified as IEEE 802.11, and the Bluetoothtechnology or the IEEE 802.15.1. Both these systems operate in the 2.4GHz Industrial, Scientific, and Medical (ISM) band (i.e., 2.400-2.4835GHz). IEEE 802.11 WLANs are designed to cover areas as vast as officesor buildings. The fundamental building block of the network is theso-called Basic Service Set (BSS), which is composed of several wirelessstations and one fixed access point. The access point providesconnection to the wired network WLANs operate at bit-rates as high as 11Mb/s and can use either a FHSS (Frequency Hopping Spread Spectrum) or aDSSS (Direct Sequence Spread Spectrum). In the case of FHSS systems,hopping sequences span over 79 channels, each one 1 MHz wide, while,DSSS systems use a 11-chip Barker sequence and their bandwidth isroughly equal to 20 MHz.

For more information regarding the IEEE signal please refer to IEEE Std802.11-1997, IEEE standard for Wireless LAN Medium Access Control (MAC)and Physical Layer (PHY) specifications.

However, Bluetooth provides interconnection of devices in the user'svicinity in a range of about 10 m. The Bluetooth system uses the ISMfrequency band at 2.4 GHz, i.e., the same as the WLAN networks occupy.The data bits are modulated using Gaussian frequency shift keying andtransmitted using frequency-hopping spread spectrum (FHSS). Bluetoothoccupy 79 MHz of the ISM band by using 79 different frequency channels,each 1 MHz wide. The Bluetooth transmitter/receiver stays 625 μs, a timeslot, in every frequency channel, i.e., the system changes channel 1600times per second. The Bluetooth transmitter is only active 366 μs out ofthe 625 μs long time slot, thus giving a maximum payload size of 366bits per time slot. Bluetooth can provide a bit-rate equal to 1 Mb/s. AFHSS scheme is used at the physical level; each master chooses adifferent hopping sequence so that piconets can operate in the same areawithout interfering with each other.

Both IEEE 802.11b and Bluetooth are designed to cope with theinterference from (a limited number of) other IEEE 802.11b or Bluetoothnetworks, respectively. In the Direct Sequence Spread Spectrum DSSS ofthe IEEE802.11(b) the power of a data signal is spread out with a PseudoNoise PN sequence over a large band, the so-called channel bandwidth W.At the receiver the DSSS signal is despreaded with the same PN sequence.The bandwidth of the received signal after despreading corresponds tothe Nyquist bandwidth B of the data signal and is determined by the datarate r_(b). A narrow-band interferer like a Continuous Wave CW or aGaussian Frequency Shift Keying GFSK modulated signal e.g. a Bluetoothsignal, that is also despreaded at the receiver can be treated within Bas Additive White Gaussian Noise AWGN.

At the receiver the DSSS signal is multiplied with the same PN sequencecorresponding to the transmitted one. This operation is usuallyperformed at a DSSS receiver in order to detect the DSSS signal andsuppress any narrow-band interference signals, like a Bluetooth GFSKmodulated signal. However, the presence of a narrow-band interferencesignal is despreaded to the channel bandwidth and can be considered aswithin the Nyquist bandwidth B as AWGN assuming that the spreading islarge enough. This leads to a decrease of the Signal to Noise ratio SNRat the input of the DSSS receiver. The desired signal can be anIEEE802.11(b) DSSS signal, so that the received signal can represent anIEEE802.11(b) DSSS signal and a narrow-band interferer signal like aBluetooth signal.

The acquisition and tracking of the IEEE802.11(b) system is the mostcritical component of the receiver, since the acquisition and trackingis partially not relying on the spreading gain. Hence, a narrow-bandinterferer is especially harmful, if e.g. the receiver is trying toacquire synchronization.

Since the IEEE 802.11b as well as the Bluetooth systems use the ISMfrequency band, interferences may occur, especially when a Bluetoothsignal hops into the band of the IEEE802.11b signal. Therefore, there isa need to cancel the influence of the narrow-band interferer orBluetooth interferer.

It is therefore an object of the invention to find and cancelnarrow-band interference signals in a transmission spectrum.

This object is solved by a method of canceling a narrow-bandinterference signal according to claim 1, and an apparatus for cancelinga narrow-band interference signal according to claim 7.

Therefore, a method of canceling a narrow-band interference signal in areceiver is provided. A reference signal ref_in is subtracted from areceived input signal IN. The phase of a result of the subtraction iscalculated on the basis of an arctangent function. An unwrap function onthe output signal from the arctangent function is performed by removingthe modulo 2Π limitation introduced with the arctangent function, inorder to produce an absolute phase representation. A frequency offset isdetermined by comparing phase representation values, which are shiftedpredetermined in time. The narrow-band interference signal is canceledbased on the result of the determined frequency offset.

The advantage of this receiving device is that its detection range iswide enough, since it is not limited by ±π.

The invention is based on the idea to use a non-linear frequencydetector to detect a narrow-band interference signal in a wide-bandsignal based on a reference signal. The output of the frequency errordetector is used to cancel the narrow-band interference signal.

These and other aspects of the invention are apparent from and will beelucidated with reference to the embodiment(s) described hereinafter.

FIG. 1 shows a possible curve of an unwrap function U_(n),

FIG. 2 shows a wrapped and an unwrapped IEEE preamble phase with α=0,

FIG. 3 shows an IEEE preamble phase with a carrier offset of oneinter-carrier spacing α=1,

FIG. 4 shows a block diagram of a preferred embodiment of a non-linearFrequency Error Detector (FED),

FIG. 5 shows a 16 sample-delayed IEEE preamble phase with no frequencyoffset (α=0), and with Δf=312.5 kHz frequency offset (one inter-carrierspacing, α=1),

FIG. 6 shows an output of a non-linear Frequency Error Detector (FED)for different carrier frequency offsets α=0, 1, 3, 7,

FIG. 7 shows a block diagram of the frequency error detector FED, and

FIG. 8 shows a block diagram of an interference eliminator means.

The interference cancellation is based on the use of interferencesuppression filters prior to the acquisition part of the IEEE802.11(b)receiver system. The interference cancellation method worksautonomously, which means that there is no feedback from the acquisitionpart of the IEEE802.11(b) receiver system. This requirement is based onthat the interference cancellation algorithm can be added to existingsystem without changing the architecture. The optimization of theparameters of the interference cancellation method should be performed.

According to an embodiment of the invention, the interferencecancellation is performed using non-linear carrier offset detector.

First of all, the non-linear frequency error detector FED is describedin detail before the interference cancellation is described. Thenon-linear frequency detector operates on the IEEE802.11a system at5×GHz and in the time domain by defining the phase on sample by samplebasis of the in-phase and quadrature components without a modulo 2πlimitation. The removal of this limitation is performed by a phaseunwrap function as described below.

The Frequency Error Detection is described with reference to Orthogonalfrequency division multiplexing (OFDM) which is a robust technique forefficiently transmitting data through a channel. The technique uses aplurality of sub-carrier frequencies (sub-carriers) within a channelbandwidth to transmit the data. These sub-carriers are arranged foroptimal bandwidth efficiency compared to more conventional transmissionapproaches, such as frequency division multiplexing (FDM), which wasteslarge portions of the channel bandwidth in order to separate and isolatethe sub-carrier frequency spectra and thereby avoid inter-carrierinterference (ICI).

The carrier frequency offset estimation is performed in the time domainby defining the phase on a sample-by-sample basis of the in-phase andquadrature components. This definition of the phase for every incomingsignal can be seen as a representation of the incoming signal in thePhase Domain, where the phase domain is defined as follows:

The phase domain represents on a sample basis the phase between everyin-phase (I(t)) and quadrature (Q(t)) component of the incoming complexsignal (x(t)) as a function of time.

In the phase domain, the subcarrier ambiguity problem will be introducedby the calculation of the phase with the arctangent function on theincoming complex (in-phase, quadrature) samples. The arctangent functionhas a range which is limited to ±π modulo 2π. The modulo 2π of thearctangent function introduces a non-linearity which causes a phaseambiguity of ±π which is due to the subcarrier ambiguity of ±½, as willbe shown in the sequel.

Let the carrier frequency offset be expressed as $\begin{matrix}{{{\Delta\quad f} = {\alpha\frac{1}{{NT}_{s}}}},{\alpha \in R}} & (1)\end{matrix}$with T_(s) the time between two samples, N the number of subcarriers ofthe OFDM signal and NT_(s) the period time of an OFDM symbol, so Eq. (1)shows the carrier frequency offset expressed in α times the intercarrierspacing (1/NT_(s)).

If we use the well-known Fourier transform pairX(f−Δf)

e ^((j2πΔft)) x(t),  (2)with x(t) the incoming OFDM signal, then Eq. (2) shows that a constantfrequency shift causes a linear increasing phase of the OFDM signalx(t). This linear behavior of the phase can be exploited to estimate, inthe time domain, the carrier frequency offset of x(t). If we want to usethe phase of x(t) we need the arctangent function $\begin{matrix}{{\psi(t)} = {{{2\quad\pi\quad\Delta\quad{ft}} + {\arg\left\{ {x(t)} \right\}}} = {{{\Delta\quad{\phi(t)}} + {\Theta(t)}} = {\arctan\left\{ \frac{Q(t)}{I(t)} \right\}\quad{{mod}\left( {2\quad\pi} \right)}}}}} & (3)\end{matrix}$If we combine Eq. (1) and Eq. (3) we obtain $\begin{matrix}{{\psi(t)} + {2\quad\pi\frac{\alpha}{{NT}_{s}}t} + {{\Theta(t)}\quad{{mod}\left( {2\quad\pi} \right)}}} & (4)\end{matrix}$Substitution of the OFDM symbol period in Eq. (4) yieldsψ(NT _(s))=α2π+Θ(NT _(s))mod(2π)  (5)The modulo (2π) part of Eq. (5) limits the value of ψ(NT_(s)) at ±π so,the maximum value of α is then $\begin{matrix}{\alpha_{\max} = {\frac{{\psi\left( {NT}_{s} \right)}_{\max} - {\Theta\left( {NT}_{s} \right)}}{2\pi} = {\pm \left( {\frac{1}{2} - \frac{\Theta\left( {NT}_{s} \right)}{2\quad\pi}} \right)}}} & (6)\end{matrix}$Eq. (6) shows that the subcarrier ambiguity is introduced by the modulo2π of the arctangent function. This modulo 2π of the arctangent functionis a nonlinear operation on ψ(t), so if we want to use the phase ψ(t) weneed the arctangent function without the modulo 2π non-linearity. Anon-linear FED is described which is able to remove this non-linearity,this removal is also a non-linear operation on the phase. By removingthe modulo 2π limitation, ψ(t) becomes a continuous function without anyphase jumps. If we look in the complex plane (in-phase component onx-axes and quadrature component on y-axes) a phase jump will occur ifthe phase moves from the first quadrant to the third or fourth quadrant(or vice versa) with an absolute value larger than π. Thusdiscontinuities in the phase occur if the phase passes the in-phase axesin the complex plane with an absolute value larger than π.

In the further part of this document, the removal of these phase jumpsis called: “phase unwrapping”. This phase unwrapping results in anabsolute phase function Φ(t), which means that the value of the phasemay be, for example, Φ(t)=23.67π and is not limited to the relativevalue of ψ(t)=−0.33π mod (2π). It is this absolute value representationΦ(t) that gives us the wide capture range of the proposed non-linearFED. It will be shown that the capture range of the FED is not limitedanymore by ±½ times the intercarrier spacing (assuming Θ(NT_(s))/2πequals zero) introduced by the arctangent function.

In the following the phase representation of a discrete OFDM signal withfrequency offset will be described. The discrete OFDM signal$\begin{matrix}{{x_{n}^{a} = {{\sum\limits_{l = {{- \frac{N}{2}} + p}}^{\frac{N}{2} - p}{B_{i}{\mathbb{e}}^{{{j2\pi}{({\frac{i}{{NT}_{s}} + \frac{\alpha}{{NT}_{s}}})}}{nT}_{s}}}} = {{\mathbb{e}}^{j\quad\alpha\frac{2\pi}{N}n}{\sum\limits_{l = {\frac{N}{2} + p}}^{\frac{N}{2} - p}{B_{i}{\mathbb{e}}^{j{({i\quad\frac{2\pi}{N}n})}}}}}}},} & (7)\end{matrix}$in which p is the number of unused subcarriers of the OFDM symbol, B_(i)is a complex signal which represents the initial phase and amplitude ofthe i-th subcarrier and n is the sample index. The phase of x_(n) ^(α)$\begin{matrix}{{\Theta_{n}^{\alpha} = {{\arg\left\{ x_{n}^{\alpha} \right\}} = {{\alpha\frac{2\quad\pi}{N}n} + {\arg\left\{ {\sum\limits_{i = {{- \frac{N}{2}} + p}}^{\frac{N}{2} - p}{B_{i}{\mathbb{e}}^{j{({i\frac{2\pi}{N}n})}}}} \right\}}}}},} & (8)\end{matrix}$is a summation of a linear function of α and the summation of the phasesof the subcarriers. This linear function of α can also be obtained for aspecific discrete OFDM preamble signal, as will be shown in thefollowing where the phase representation of the IEEE P802.11a/D7.0preamble (further referred to as: “IEEE preamble”) is used in W-LAN OFDMsystems. This IEEE W-LAN OFDM system uses the following figs.; N=64points (I)FFT, with a sample frequency of F_(s)=20 MHz (T_(s)=50 ns) andp=6 unused subcarriers, substituting these figs. in Eq. (7) and Eq. (8)we obtain $\begin{matrix}{{x_{n}^{\alpha} = {{\mathbb{e}}^{j\quad\alpha\frac{\pi}{32}n}{\sum\limits_{i = {- 26}}^{26}{B_{i}{\mathbb{e}}^{j{({i\frac{\pi}{32}n})}}}}}},} & (9)\end{matrix}$for the OFDM signal and $\begin{matrix}{{\Theta_{n}^{\alpha} = {{\alpha\quad\frac{\pi}{32}n} + {\arg\left\{ {\sum\limits_{i = {- 26}}^{26}{B_{i}{\mathbb{e}}^{j{({i\quad\frac{\pi}{32}n})}}}} \right\}}}},} & (10)\end{matrix}$for the phase of the OFDM signal.

The preamble is defined in IEEE P802.11a/D7.0. It is a short OFDM symbolconsisting of 12 subcarriers which are modulated by the elements S_(i)of the sequence given by:S=S ⁻¹ , . . . , S _(i)=√{square root over(13/6)}(0,0,1+j,0,0,0,−1−j,0,0,0,1+j,0,0,0,−1−j,0,0,0,−1−j,0,0,0,1+j,0,0,0,0,0,0,0,−1−j,0,0,0,−1−j,0,0,0,1+j,0,0,0,1+j,0,0,0,j1+j,0,0,0,1+j,0,0),i=0,1, . . . , 25,26  (11)with the indexes (−26, . . . ,26) referring to the subcarrier numbers ofthe OFDM symbol. The multiplication by the factor √{square root over(13/6)} is needed to normalize the average power because the IEEEpreamble only uses 12 out of the 52 subcarriers. It can be seen from Eq.(11) that only the subcarriers with an index which is a multiple of fourare non-zero, so substitution of m=i/4 in Eq. (9) and exchanging theelements B_(i) with the elements S_(i) yields, $\begin{matrix}{{p_{n}^{\alpha} = {{\sqrt{13/6}{\mathbb{e}}^{j\quad\alpha\quad\frac{\pi}{32}n}{\sum\limits_{m = {- 6}}^{6}{S_{m}{\mathbb{e}}^{j\quad m\quad\frac{\pi}{8}n}\quad m}}} \neq 0}},} & (12)\end{matrix}$the presentation of the IEEE preamble and $\begin{matrix}{{{\overset{\sim}{\phi}}_{n}^{\alpha} = {{{\alpha\quad\frac{\pi}{32}n} + {\arg\left\{ {\sum\limits_{m = {- 6}}^{6}{S_{m}{\mathbb{e}}^{j\quad m\frac{\pi}{8}n}}} \right\}\quad m}} \neq 0}},} & (13)\end{matrix}$the phase of this IEEE preamble. The subcarrier S₀ is equal to zero(DC-subcarrier), so the index m=0 is not used for the IEEE preamble. Eq.(12) shows that if m=±1 the fundamental frequency F₀=1/NT_(s) in theOFDM signal $\begin{matrix}{F_{p} = {{4F_{0}} = {{4\frac{1}{64T_{s}}} = {\frac{1}{16T_{s}}.}}}} & (14)\end{matrix}$

Then the period time or periodicity of the preamble $\begin{matrix}{T_{p} = {\frac{1}{F_{p}} = {{\frac{1}{4}T_{0}} = {16{T_{s}.}}}}} & (15)\end{matrix}$is 16 samples (not 64 as the OFDM signal), so the IEEE preamble has aduration of 16 samples (800 ns).

If we look somewhat closer at the components of the sequence S we seethatS _(m) =−S _(−m)

S _(m) e ^(jβm) +S _(−m) e ^(−jβm) =j2S _(m) sin(B _(m)) m=1,3,5,  (16)S _(m) =S _(−m)

S _(m) e ^(jβm) +S _(−m) e ^(−jβm)=2S _(m) cos(B _(m)) m=2,4,6,with β_(m) an arbitrary number. Using this goniometric equality in Eq.(12) yields $\begin{matrix}{{p_{n}^{\pi} = {2\sqrt{13/6}{\mathbb{e}}^{{j\alpha}\frac{\pi}{32}n}\left\{ {{S_{2}{\cos\left( {2\frac{\pi}{8}n} \right)}} + {S_{4}{\cos\left( {4\frac{\pi}{8}n} \right)}} + {S_{6}{\cos\left( {6\frac{\pi}{8}n} \right)}} + {j\left\lbrack {{S_{1}{\sin\left( {\frac{\pi}{8}n} \right)}} + {S_{3}{\sin\left( {3\frac{\pi}{8}n} \right)}} + {S_{5}{\sin\left( {5\frac{\pi}{8}n} \right)}}} \right\rbrack}} \right\}}},} & (17)\end{matrix}$and with $\begin{matrix}{{S_{1} = {S_{2} = {{- \left( {1 + j} \right)} = {{- \sqrt{2}}{\mathbb{e}}^{j\frac{\pi}{4}}}}}}{S_{3} = {S_{4} = {S_{5} = {S_{6} = {\left( {1 + j} \right) = {\sqrt{2}{{\mathbb{e}}^{j\frac{\pi}{4}}.}}}}}}}} & (18)\end{matrix}$the representation of the IEEE preamble becomes $\begin{matrix}{p_{n}^{\pi} = {2\sqrt{13/6}{\mathbb{e}}^{j{({{\alpha\frac{\pi}{32}n} + \frac{\pi}{4}})}}{\left\{ {{- {\cos\left( {2\frac{\pi}{8}n} \right)}} + {\cos\left( {4\frac{\pi}{8}n} \right)} + {\cos\left( {6\frac{\pi}{8}n} \right)} + {j\left\lbrack {{- {\sin\left( {\frac{\pi}{8}n} \right)}} + {\sin\left( {3\frac{\pi}{8}n} \right)} + {\sin\left( {5\frac{\pi}{8}n} \right)}} \right\rbrack}} \right\}.}}} & (19)\end{matrix}$

The phase of the IEEE preamble $\begin{matrix}\begin{matrix}{{{{\overset{\sim}{\phi}}_{n}^{\alpha}\frac{\pi}{4}} + {\alpha\frac{\pi}{32}n} + \theta_{n}},} \\{\theta_{n} = {\arctan\left\{ \frac{{- {\sin\left( {\frac{\pi}{8}n} \right)}} + {\sin\left( {3\frac{\pi}{8}n} \right)} + {\sin\left( {5\frac{\pi}{8}n} \right)}}{{- {\cos\left( {2\frac{\pi}{8}n} \right)}} + {\cos\left( {4\frac{\pi}{8}n} \right)} + {\cos\left( {6\frac{\pi}{8}n} \right)}} \right\}}}\end{matrix} & (20)\end{matrix}$is a summation of an initial phase (π/4), a linear changing phase as afunction of the carrier frequency offset $\alpha\frac{\pi}{32}n$and an arctangent function performed on a summation of sinusoids withmultiple frequencies (θ_(n)). The behavior of θ_(n) is not easy todetermine analytically, so it is obtained via simulations where thein-phase and quadrature components for every sample of the IEEE preamble(periodic with 16) in the upper part (complex plane representation) andthe arctangent values of the IEEE preamble in the lower part (phasedomain representation) are determined. It can be seen that a modulo 2πphase correction needs to be performed between samples 1,2 (mod 16), 6,7(mod 16), 10,11 (mod 16) and 13,14 (mod 16), because between theseconsecutive samples the phase of the IEEE preamble passes the in-phaseaxes with an absolute value larger than π.

The 2π phase correction is performed by an unwrap function (U_(n)) andcan be described as follows: The unwrap function (U_(n)) accumulates ktime 2π, where k depends on the wrapped function to which U_(n) isapplied. k will be increased by one if the difference between the lastcorrected sample and the current sample is smaller than −π. k will bedecreased by one if the difference between the last corrected sample andthe current sample is larger than π.

FIG. 1 shows a possible curve of U_(n), every function value U_(n) is amultiple of 2π (k times 2π) and depends on the wrapped function.Applying the unwrap function Un to the wrapped phase {tilde over(φ)}_(n) ^(α) of the IEEE preamble yields $\begin{matrix}{{\phi_{n}^{\alpha} = {\frac{\pi}{4} + {\alpha\frac{\pi}{32}n} + \theta_{n}}},} & (21)\end{matrix}$the unwrapped phase of the IEEE preamble. The wrapped phase {tilde over(φ)}_(n) ⁰ and the unwrapped phase φ_(n) ⁰ are represented by the solidline and dotted line respectively, in FIG. 7. It can be seen from FIG. 2that the unwrapped phase φ_(n) ⁰ behaves like a sinewave. Eq. (21) showsthat the sinewave behavior of φ_(n) ^(α) with α=0, is the behavior ofθ_(n). If we take a closer look at this sinewave behavior we are able todetermine an approximation of $\begin{matrix}{{\phi_{n} \approx {\frac{7\pi}{4}{\sin\left( {\frac{\pi}{8}n} \right)}}},} & (22)\end{matrix}$and Eq. (21) can be approximated with $\begin{matrix}{\phi_{n}^{\alpha} \approx {\frac{\pi}{4} + {\alpha\frac{\pi}{32}n} + {\frac{7\pi}{4}{{\sin\left( {\frac{\pi}{8}n} \right)}.}}}} & (23)\end{matrix}$

If we look at Eq. 20, we see that the carrier frequency offset gives alinear increase of the phase. If we are able to determine the angle ofdirection of the wrapped phase {tilde over (φ)}_(n) ^(α), then we knowthe frequency offset represented by α. By applying the unwrap functionU_(n) to {tilde over (φ)}_(n) ^(α), we obtain the unwrapped phase φ_(n)^(α) shown by Eq. (21). If we look at FIG. 2, we can see that theunwrapped phase φ_(n) ¹ increases linearly due to the carrier frequencyoffset Δf=312.5 kHz of one intercarrier spacing (α=1).

As mentioned earlier, the behavior of θ_(n) is approximated with asinewave, and it can be seen from FIG. 3 that this approximation canalso be used in the case α≠0.

The unwrapping and the subsequent detection of the angle of direction ofthe wrapped phase {tilde over (φ)}_(n) ^(α) are performed by thenon-linear FED and will be described in detail in the following. Thecarrier frequency offset estimation, as stated before, is performed inthe time domain by defining the phase on a sample-by-sample basis of thein-phase and quadrature components without the modulo 2π limitation. Theremoval of this limitation is performed by the phase unwrap function.

If we look at FIG. 3, it can be seen that the angle of direction can bedefined by taking the difference between two function values which areshifted in time and have equal values in the case that there is nocarrier frequency offset (α=0). It can be seen from Eq. 15 and Eq. 23that the periodicity of {tilde over (φ)}_(n) ^(α) and φ_(n) ^(α) equals16, so every two function values which are 16 samples apart from eachother have the same value, as can also be verified graphically in FIG.2. The difference between φ_(n) ^(α) and φ_(n+16) ^(α) is constant forevery n and proportional to the carrier frequency offset. If thisconstant value is contaminated by noise, the influence of this noise canbe decreased by averaging the samples. All of the above mentionedoperations with the signal names are shown in FIG. 4, the block diagramof the non-linear FED.

The signal p_(n) ^(α) described by Eq. 19 and shown in FIG. 4 for α=0 isthe input signal for the “complex phase” block. The output signal of the“complex phase” block is the wrapped phase $\begin{matrix}{{{\overset{\sim}{\phi}}_{n}^{\alpha} = {\frac{\pi}{4} + {\alpha\frac{\pi}{32}n} + \theta_{n}}},{{mod}\left( {2\pi} \right)}} & (24)\end{matrix}$of p_(n) ^(α) and is shown as the solid line in FIG. 2 with no carrierfrequency offset (α=0).

Applying the unwrap function U_(n) to the input signal {tilde over(φ)}_(n) ^(α) yields $\begin{matrix}{{\phi_{n}^{\alpha} \approx {\frac{\pi}{4} + {\alpha\frac{\pi}{32}n} + {\frac{7\pi}{4}{\sin\left( {\frac{\pi}{8}n} \right)}}}},} & (25)\end{matrix}$at the output of the “phase unwrap” block. This unwrapped phase signalis shown as the dotted lines in FIG. 2 for α=0 and in FIG. 3 for α=1.

The output signal of the “Z^(−N)” block is the delayed version of theunwrapped phase signal $\begin{matrix}{{\phi_{n - D}^{\alpha} \approx {\frac{\pi}{4} + {\alpha\frac{\pi}{32}\left( {n - D} \right)} + {\frac{7\pi}{4}\sin\left\{ {\frac{\pi}{8}\left( {n - D} \right)} \right\}}}},} & (26)\end{matrix}$with D the number of delayed samples. With some goniometric equalities,Eq. 26 can be rewritten as $\begin{matrix}{{\phi_{n - D}^{\alpha} \approx {\frac{\pi}{4} + {\alpha\frac{\pi}{32}\left( {n - D} \right)} + {\frac{7\pi}{4}\left\lbrack {{{\sin\left( {\frac{\pi}{8}n} \right)}{\cos\left( {\frac{\pi}{8}D} \right)}} - {{\cos\left( {\frac{\pi}{8}n} \right)}{\sin\left( {\frac{\pi}{8}D} \right)}}} \right\rbrack}}},} & (27)\end{matrix}$substituting D=16 (the period of the IEEE preamble) in Eq. 27 yields$\begin{matrix}{{\phi_{n - 16}^{\alpha} \approx {{\left( {1 - {2\alpha}} \right)\frac{\pi}{4}} + {\alpha\frac{\pi}{32}n} + {\frac{7\pi}{4}{\sin\left( {\frac{\pi}{8}n} \right)}}}},} & (28)\end{matrix}$and is shown in FIG. 5 for α=0 and α=1.

The output signal of the “subtract” block is the unwrapped phasedifference signal $\begin{matrix}{{\Delta\phi}_{n,D}^{\alpha} \approx {\frac{\pi}{4} + {\alpha\frac{\pi}{32}n} + {\frac{7\pi}{4}{\sin\left( {\frac{\pi}{8}n} \right)}} - {\quad{{\left\lbrack {\frac{\pi}{4} + {\alpha\frac{\pi}{32}\left( {n - D} \right)} + {\frac{7\pi}{4}\sin\left\{ {\frac{\pi}{8}\left( {n - D} \right)} \right\}}} \right\rbrack = {{\alpha\frac{\pi}{32}D} + {\frac{7\pi}{4}\left\{ {{\left\lbrack {1 - {\cos\left( {\frac{\pi}{8}D} \right)}} \right\rbrack{\sin\left( {\frac{\pi}{8}n} \right)}} + {{\sin\left( {\frac{\pi}{8}D} \right)}{\cos\left( {\frac{\pi}{8}n} \right)}}} \right\}}}},}}}} & (29)\end{matrix}$and for D=16 Eq. 29 becomes $\begin{matrix}{{{\Delta\phi}_{n,16}^{\alpha} \approx {\alpha\frac{\pi}{2}}},} & (30)\end{matrix}$The sinewave behavior in the beginning of the curve is a switch-onphenomenon because the first 16 samples of φ_(n−16) ^(α) are equal tozero. These first 16 samples cannot be used for the detection of thecarrier frequency offset, so in the case of the IEEE OFDM system, only144 out of the 160 samples can be used.

The output signal of the “mean estimator” block is the unwrapped phasedifference signal average with a sliding window of 144 samples. The meanestimator takes the sum of the last 144 samples and divides this numberby 144. The output of the mean estimator, also the FED output, is shownin FIG. 6 for different values of α=0, 1, 3, 7.

The value of the 160^(th) sample (sample number 159) is the exactrepresentation of the carrier frequency offset, because the switch-onphenomenon has no influence on that sample anymore.The unwrap function Un increases or decreases the 2π counter k dependingon the phase difference between the last corrected sample and thecurrent sample. If this phase difference is larger than the absolutevalue |π| due to carrier frequency offset (large α), noise or any othercause than the arctangent function, the FED will not be able to correctthis. This limitation is the capture range of the non-linear FED and canbe obtained by finding the n, whereby φ_(n) ^(α=0) shows a maximum phasechange $\begin{matrix}{{{{\max\limits_{n}\left\{ \left. \frac{\mathbb{d}\phi_{n}^{\alpha}}{\mathbb{d}n} \right|_{\alpha = 0} \right\}} \approx {\max\limits_{n}\left\{ {\frac{7\pi^{2}}{32}{\cos\left( {\frac{\pi}{8}n} \right)}} \right\}}} = \frac{7\pi^{2}}{32}},{{{for}\quad n} = {0\quad{{mod}(8)}}}} & (31)\end{matrix}$substituting this in Eq. 29 with D=1 (consecutive samples) gives,$\begin{matrix}{{{\Delta\phi}_{0,1}^{\alpha_{\max}} \approx {{\alpha_{\max}\left( \frac{\pi}{32} \right)} + {\frac{7\pi}{4}{\sin\left( \frac{\pi}{8} \right)}}}} = {{\pi\left\lbrack {\frac{\alpha_{\max}}{32} + {\frac{7}{4}{\sin\left( \frac{\pi}{8} \right)}}} \right\rbrack}.}} & (32)\end{matrix}$With the limitation of ±π between two consecutive samples, the capturerange αmax will then be $\begin{matrix}{{{\pi\left\lbrack {\frac{\alpha_{\max}}{32} + {\frac{7}{4}{\sin\left( \frac{\pi}{8} \right)}}} \right\rbrack} = \left. {\pm \pi}\Rightarrow{\alpha_{\max} \approx {\pm {32\left\lbrack {1 - {\frac{7}{4}\sin\left( \frac{\pi}{8} \right)}} \right\rbrack}} \approx {\pm 10}} \right.},} & (33)\end{matrix}$this number is not the exact capture range due to the approximation bythe sinewave. It can be seen from Eq. 33 that the capture range islimited by the maximum phase jump in the sinewave part of φ_(n) ^(α).This phase jump between two consecutive samples can be decreased by i.aover-sampling. This over-sampling increases the capture range. A factorof two over-sampling yields $\begin{matrix}{{\alpha_{\max} \approx {\pm {64\left\lbrack {1 - {\frac{7}{4}{\sin\left( \frac{\pi}{16} \right)}}} \right\rbrack}} \approx {\pm 42}},} & (34)\end{matrix}$this number is not the exact capture range due to the approximation bythe sinewave.

The theoretical figs. obtained, until now, for the non-linear FED withthe IEEE preamble are:Output value is${{\Delta\quad\phi_{n,16}^{\alpha}} \approx {\alpha\quad\frac{\pi}{2}}},$

-   Capture range without over-sampling is: α_(max)≈±10 (Δf_(max)≈±3.2    MHz)-   Capture range with over-sampling by 2 is: α_(max)≈±42    (Δf_(max)≈±13.1 MHz)    Now the interference cancellation using the above frequency error    detector (but for an IEEE 802.11b signal at 2.4×GHz) is described in    more detail:

According to an embodiment of the invention, the interferencecancellation is performed for Bluetooth signals. The Bluetooth signal isGFSK modulated with a modulation index of m=0.28 . . . 0.35 and abandwidth bit duration product that equals BF=0,5. The carrier frequencypeak deviation is chosen to be$f_{d} = {{\frac{m}{2}r_{b}} = \frac{m}{2\quad T}}$where r_(b) represents the bit rate, which equals 1 Mbps. Theinformation bits b_(n) are shaped by a Gaussian filter and thus${{b_{g}(t)} = {\sum\limits_{n = {- \infty}}^{\infty}{I_{n}{q\left( {t - {n\quad T}} \right)}}}},$with I_(n) is equal to 1 if b_(n) is equal to one and −1 if b_(n) isequal to zero and where${q(t)} = {K{\int_{0}^{T}{{\mathbb{e}}^{- {\beta{({t - \quad\frac{T}{2}})}}^{2}}{\mathbb{d}t}}}}$represents the Gaussian pulse shape with$K = {B\quad T\sqrt{\frac{2\quad\pi}{\ln\quad 2}}}$ and$\beta = {\frac{2}{\ln\quad 2}{\left( {\pi\quad B\quad T} \right)^{2}.}}$The Bluetooth interference signal can be written asi_(b)(t) = 𝕖^(j  2  π{f_(d)∫_(−∞)^(t)b_(g)(α)𝕕α + f_(c)t})${i_{b}(t)} = {\mathbb{e}}^{j\quad 2\quad\pi{\{{{\underset{2}{m}\quad r_{b}{\int_{- \infty}^{t}{{b_{g}{(\alpha)}}{\mathbb{d}\alpha}}}} + {f_{c}t}}\}}}$with the time-varying phase $\begin{matrix}{{{\arg\left\{ {i_{b}(t)} \right\}} = {{\Phi(t)} = {{m\quad\pi\quad r_{b}\quad{\int_{- \infty}^{t}{{b_{g}(\alpha)}{\mathbb{d}\alpha}}}} + {2\quad\pi\quad f_{c}t}}}}{{\Phi(t)} = {{m\quad\pi\quad r_{b}{\int_{- \infty}^{t}{\left\lbrack {\sum\limits_{n = {- \infty}}^{\infty}{I_{n}{q\left( {\alpha - {n\quad T}} \right)}}} \right\rbrack{\mathbb{d}\alpha}}}} + {2\quad\pi\quad f_{c}t}}}} & (35)\end{matrix}$If we look at the derivative $\begin{matrix}{{\Phi(t)} = {\frac{\mathbb{d}{\Phi(t)}}{\mathbb{d}t} = {{m\quad\pi\quad r_{b}{b_{g}(t)}} + {2\quad\pi\quad f_{c}}}}} & (36)\end{matrix}$of the time varying phase of Eq. (35), which represents the frequency ofthe FSK modulated Bluetooth signal. The first term of Eq (36) is varyingwith time while the second term is a constant value that is proportionalwith the carrier frequency of the Bluetooth FSK modulated signal. IfΦ(t) is normalized on 2πr_(b) and we assume that f_(c) is relevant withdistances kr_(b), (where k is an integer) to the carrier frequency ofthe desired DSSS signal. Therefore, $\begin{matrix}{{\overset{\_}{\Phi(t)} = \frac{{m\quad\pi\quad r_{b}{b_{g}(t)}} + {2\quad\pi\quad f_{c}}}{m\quad\pi\quad r_{b}}}{\overset{\_}{\Phi(t)} = {{{\frac{m}{2}{b_{g}(t)}} + k} = {{\frac{m}{2}{\sum\limits_{n = {- \infty}}^{\infty}{I_{n}{q\left( {t - {n\quad T}} \right)}}}} + k}}}} & (37)\end{matrix}$with k= . . . , −2, −1, 0, 1, 2, . . .

Φ(t) represents the normalized phase of only the Bluetooth signal.Therefore, no phase transitions due to the desired DSSS signal, i.e. theIEEE802.11(b) signal, are taken into account. The value of I_(n) equals±1 in a pseudo random behavior due to scrambling of the data bits b_(n)(PN sequence). This means that the first term of Eq. (37) has zero mean,so that the value of k is a measure for the carrier frequency of theBluetooth signal, i.e. the carrier frequency of the narrow-bandinterferer to be cancelled. Therefore, the value of k will give anindication of the frequency that is to be cancelled.

FIG. 8 shows a block diagram of an interference eliminator implementingthe above principles. The eliminator comprises a non-linear carrieroffset detector, i.e. a frequency error detector FED, and a subtractingunit SUB. The subtracting unit receives a reference signal ref_in andthe received signal IN as inputs, and performs a subtraction operationi.e. the received signal IN is subtracted from the reference signalref_in. The result of this subtraction is used as input signal of thenon-linear carrier offset detector. Here, we assume that the receivedsignal corresponds to the signal transmitted by the transmitter plus thenarrow-band interferer. If the reference signal is known and thetransmitter transmits this reference signal ref_in, then the result ofthe subtraction of the received signal from the reference signal willcorrespond to the narrow-band interferer, i.e. that signal that wasintroduced by the transmission of the signal transmitted by thetransmitter. The set up and the function of the non-linear carrieroffset detector or the frequency error detector FED has been describedabove with reference to FIG. 1 to 7 for a IEEE802.11a system but canalso be used for a IEEE802.11b system with 2.4×GHz. The output of thenon-linear carrier offset detector represents the above mentionedk-values according to which the carrier frequency of the narrow-bandinterferer is determined. The subtracting unit SUB as well as thefrequency detector (in particular the unwrap function) can be put on ahold if no reference signal is available.

The actual interference cancellation can be performed by using the valueof k to select a proper filter out of 2k+1 different filters in a filterbank. These two 2k+1 filters can have the optimal Wiener solution forfiltering out the particular narrowband interference signal. Theadvantage of this filter-bank is that the filters could be small with afew taps because the shape and position of the interference is exactlyknown.

An alternative solution is to generate a signal, having same frequencyas the determined carrier frequency of the narrow-band interferer, andsubtract it from the distorted desired wide-band signal, so that thesubtraction results in the desired wide-band signal.

The reference signal is considered as a transmitted signal, which isknown to the receiver. The selection of a reliable reference signal isnot trivial. In most practical situations this reference signal is noteasy available. One solution is to use the training signal of theIEEE802.11b. This signal is known but it is merely used as a trainingsequence, for the cases that the narrow-band interferer hops into one ofthe IEEE802.11b bands after the training sequence of the IEEE802.11b hasbeen transmitted, it is not possible to use the training sequence asreference signal anymore and the interference cancellation can not beperformed accurately. However, as soon as the training sequence istransmitted again, the interference cancellation can also be performedagain.

The embodiments of the invention are described with an IEEE 802.11bsignal as wide-band signal and a Bluetooth signal as narrow-bandinterferer. However, the principles of the invention may be applied toevery wired or wireless narrow-band signal introducing a frequencyoffset to a desired wide-band signal.

The above embodiments can be implemented by hardware or by software. Itshould be noted that the above-mentioned embodiments illustrate ratherthan limit the invention, and that those skilled in the art will be ableto design many alternative embodiments without departing from the scopeof the appended claims. In the claims, any reference signs placedbetween parentheses shall not be construed as limiting the claim. Theword “comprising” does not exclude the presence of elements or stepsother than those listed in a claim. The word “a” or “an” preceding anelement does not exclude the presence of a plurality of such elements.In the device claim enumerating several means, several of these meanscan be embodied by one and the same item of hardware. The mere fact thatcertain measures are recited in mutually different dependent claims doesnot indicate that a combination of these measures cannot be used toadvantage.

Furthermore, any reference signs in the claims shall not be construed aslimiting the scope of the claims.

1. A method of canceling a narrow-band interference signal in a receiver, comprising the steps of: subtracting a reference signal (ref_in) from a received input signal (in); calculating the phase of a result of the subtraction on the basis of an arctangent function, performing an unwrap function on the output signal from the arctangent function, by removing the modulo 2Π limitation introduced with the arctangent function, thereby producing an absolute phase representation, determining a frequency offset by comparing phase representation values which are shifted predetermined in time, and canceling the narrow-band interference signal based on the result of the determined frequency offset.
 2. A method according to claim 1, characterized in that the unwrap function accumulates k times 2Π, where k depends on the wrapped function so that k will be increased by 1 if the difference between the last corrected sample and the current sample is smaller than −Π, and k will be decreased by 1 if the difference between the last corrected sample and the current sample is greater than Π.
 3. A method according to claim 1, characterized in that the subtracting step can be hold a predetermined period of time, if there is no reference signal available to perform the subtraction.
 4. A method according to claim 2, characterized in that the unwrap function can be hold a predetermined period of time, if there is no reference signal available to perform the unwrap function.
 5. A method according to claim 2, characterized in that the canceling the narrow-band interference signal is performed by selecting a filter from within a filter-bank based on the value of k.
 6. A method according to claim 2, characterized in that the canceling the narrow-band interference signal is performed by generating a second narrow-band signal, which corresponds to the narrow-band interference signal, and by subtracting the second narrow-band signal from the distorted desired wide-band signal.
 7. An apparatus characterized in that the apparatus comprises a subtracting unit (SU) for subtracting a reference signal (ref_in) from a received input signal (in); a complex phase calculator for calculating the phase of a result of the subtraction signal on a sample-by-sample basis of the in-phase and quadrature components of the signal and performing an arctangent function on the in-phase and quadrature components of the incoming signal, a phase unwrap module for removing discontinuities in the phase if the phase passes the in-phase axes in the complex plane with an absolute value greater than Π, a comparator module arranged to compare the difference in phase signal values at predetermined time intervals, the difference in said values representing an frequency offset in the subtracting signal, and a canceling means for canceling the narrow-band interference signal based on the result of the determined frequency offset.
 8. An apparatus according to claim 7, characterized in that the phase unwrap module is adapted to accumulate k times 2Π, where k depends on the wrapped function so that k will be increased by 1 if the difference between the last corrected sample and the current sample is smaller than −Π, and k will be decreased by 1 if the difference between the last corrected sample and the current sample is greater than Π.
 9. An apparatus according to claim 8, characterized in that the canceling means comprises a filter-bank, wherein the narrow-band interference signal is canceled by selecting a filter from within said filter-bank based on the value of k.
 10. An apparatus according to claim 7, characterized in that the canceling means comprises a generating means for generating a second narrow-band signal, which corresponds to the narrow-band interference signal, and a subtracting means for subtracting the second narrow-band signal from the distorted desired wide-band signal. 